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 2007-03-03, 11:38 #1 AntonVrba     Jun 2005 2×72 Posts Help needed Please help in understanding the series 1, 2, 6, 8, 22, 32, 84, 128,... that is Sloane A081672 and is titled "Expansion of exp(2x)-exp(0)+BesselI_0(2x)." I do not understand the term "expansion" in above context. Further do you recognize the following series in the same contents? 1,3,13, 27, 105, 243, 889, 3^7,.... 1,4, 22, 64, 310, 1024, 4636, ... 1,5, 33, 125, 721, 3125, 16905, ... These series I generate from any prime but in modula p. best regards Anton Last fiddled with by AntonVrba on 2007-03-03 at 11:39
 2007-03-05, 17:52 #2 ewmayer ∂2ω=0     Sep 2002 República de California 267318 Posts Glanced at the OEIS entry - it mentions an "Inverse binomial transform", so my guess is that that leads to an oo series, and these are the coefficients. But don't take my (speculative) word for it - suggest you e-mail the entry author, whose e-address is attached to the entry.
2007-03-05, 18:06   #3
m_f_h

Feb 2007

24×33 Posts

Quote:
 Originally Posted by AntonVrba Please help in understanding the series 1, 2, 6, 8, 22, 32, 84, 128,... that is Sloane A081672 and is titled "Expansion of exp(2x)-exp(0)+BesselI_0(2x)." I do not understand the term "expansion" in above context. Further do you recognize the following series in the same contents? 1,3,13, 27, 105, 243, 889, 3^7,.... 1,4, 22, 64, 310, 1024, 4636, ... 1,5, 33, 125, 721, 3125, 16905, ... These series I generate from any prime but in modula p.
I don't understand it, either; I suspect there might be error since why write exp(0) instead of 1 ?
I don't recognize your sequences either - modula p means "mod p" ?
then for primes smaller than 100 I dont understand how to get values > 100, and 'mod p' should give different things once you have a number larger than p (and before there's no use in saying mod p)...

 2007-03-06, 10:55 #4 AntonVrba     Jun 2005 2×72 Posts Friends, thanks the problem is solved see here

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